The work described in Point 3 of France Dacar's recent message looks very much like a special case of work of Andreka and Nemeti and Guitart and Lair. The basic references are given below in BibTeX input form, which is (I fondly believe) self-explanatory: @ARTICLE{ author = "Andreka, H. and I. Nemeti", title = "Formulas and ultraproducts in categories", journal = "Beit. zur Alg. und Geom.", volume = 8, year = 1979 } @ARTICLE{ author = "Guitart, Ren\'e and Christian Lair", title = "Calcul Syntaxique des Mod\`eles et Calcul des Formules Internes", journal = diagrammes, year = "1980", volume = "4", } I do not have the Andreka and Nemeti article. These articles are also relevant: @ARTICLE{ author = "Guitart, Ren\'e and Christian Lair", title = "Limites et Co-limites pour Repre\-senter les For\-mu\-les", journal = diagrammes, year = "1982", volume = "7", } @ARTICLE{ author = "Guitart, Ren\'e", title = "On the Geometry of Computations (I)", journal = cahiers, year = "1986", volume = "27", pages = "107--136", } -- Charles Wells, Department of Mathematics, Case Western Reserve University 10900 Euclid Avenue, Cleveland OH 44106-7058, USA Phone 216 368 2880 or 216 774 1926 FAX 216 368 5163 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++